Distributed Tomographic Reconstruction with Quantization

TL;DR

A decentralized Alternating Directions Method of Multipliers with configurable quantization is introduced, which is highly scalable and can efficiently reconstruct images while adapting to available resources.

Abstract

Conventional tomographic reconstruction typically depends on centralized servers for both data storage and computation, leading to concerns about memory limitations and data privacy. Distributed reconstruction algorithms mitigate these issues by partitioning data across multiple nodes, reducing server load and enhancing privacy. However, these algorithms often encounter challenges related to memory constraints and communication overhead between nodes. In this paper, we introduce a decentralized Alternating Directions Method of Multipliers (ADMM) with configurable quantization. By distributing local objectives across nodes, our approach is highly scalable and can efficiently reconstruct images while adapting to available resources. To overcome communication bottlenecks, we propose two quantization techniques based on K-means clustering and JPEG compression. Numerical experiments with benchmark images illustrate the tradeoffs between communication efficiency, memory use, and reconstruction accuracy.

Figures (8)

• Figure 1: Illustration of the tomographic data acquisition setup. The sample is illuminated with x-rays and rotated while projections are captured at various angles, typically ranging from 0° to 180°. These projections, recorded by the detector, are compiled into a sinogram that are correlated with the intensity of x-rays transmitted through the object at each angle.
• Figure 2: On the left, we illustrate the memory and communication requirements for dADMM within a single node. On the right, we plot these requirements as the number of nodes increases, for a $2048 \times 2048$ tomographic reconstruction image. This includes data with similar dimensions, such as 2048 rotation angles and 2048 detector pixels.
• Figure 3: Samples of the true Phantom and Barbara images, along with their corresponding sinograms, used for assessing the performance of the proposed algorithm.
• Figure 4: Comparison of reconstructed Phantom and Barbara images using CTR and DTR with 2 and 10 nodes against the ground truth. The values in the bottom left corner of each image indicate the RMSE and PSNR of that image compared to the Ground Truth image shown in the leftmost column.
• Figure 5: RMSE between the reconstructions and the true image as a function of compression levels for both methods.